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Let S be a non-empty subset of R. Consid...

Let S be a non-empty subset of R. Consider the following statement: P: There is a rational number `x in S` such that `x"">""0`.
Which of the following statements is the negation of the statement P ?
There is no rational number `x in S` such that `xlt=0` (9)
Every rational number `x in S` satisfies `xlt=0` (18)
`x in S` and `xlt=0=>x` (27) is not rational
There is a rational number `x in S` such that `xlt=0` (36)

Text Solution

Verified by Experts

`x in S`
`x > 0`
`x in S; x <= 0`
option 2 is correct
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Knowledge Check

  • Let S be non-empty subset of R. consider the following statement: P: There is a rational number x ne S " such that " x gt 0 Which of the following statements is the negation of the statement P ?

    A
    Every rational number `x ne S ` such that `x le 0`
    B
    `x in S and x le 0 Rightarrow x` is not rational
    C
    There is a rational number `x in S " such that " x le 0`
    D
    There is no rational number `x in S " such that x le 0`

  • Let S be a non-empty subset of R. consider the following statement : P: There is a rational number xinS such that xgt0. which of the following statements is the negation of the statement P?

    A
    `x in S` and `x le 0 rArr x` is not rational
    B
    There is rational number `x in S` such that `xle0`.
    C
    There is no rational number `x in S` such that `xle0`.
    D
    Every rational number `x in S` satisfies `xle0`

  • Let S be a non-empty subset of R. Consider the statement P : There is a rational number x in S such that x gt 0 . Which of the following statements is the negation of the statement P ?

    A
    There is a rational number `x in S` such that `x le 0`
    B
    There is no rational number `x in S` such that `x le 0`
    C
    Every rational number `x in S` satisfies `x le 0`
    D
    `x in S` and `x le 0 rArr x` is not rational